Is there any example of using Q-learning with big data?
Or in RL does the agent built its own dataset?


Essentially this is the case.

RL is a very general learning mechanism, based on trial-and-error. You could create an environment where the agent's goal is to correctly predict classification or regression problems, where the agent is rewarded for getting close to the correct prediction. However, these problems are most often better addressed using supervised learning techniques. Using RL in such cases will most of the time make the learning slower, less efficient and less accurate.

The relationship between RL and supervised learning is more about how RL generates the target data for learning. In some cases, such as Deep Q Learning (DQN), you can see quite clearly from looking at the algorithm or code, that the RL agent contains a supervised learning component. The "supervised learning" in DQN learns a regression problem to predict the action values for the current agent's target policy. Whilst the outer RL logic that contains this supervised learning model, is built around testing and changing that behaviour in order to act optimally in the longer term.

Using RL to predict from a big data set would involve using the same kind of supervised learning model on the inside, with RL using that to guess at the correct result, and sometimes choosing to guess at some other random prediction instead. This guessing process is extra processing, plus it will add noise and variance to the error signal used to train the model. In a few cases, this might even be helpful, but in the majority of cases studied for regression and classification tasks, it will result in a poorer training process, less accurate model, or both.